The constraining effect of gas and the dark matter halo on the vertical stellar distribution of the Milky Way

Abstract

We study the vertical stellar distribution of the Milky Way thin disk in detail with particular focus on the outer disk. We treat the galactic disk as a gravitationally coupled, three-component system consisting of stars, atomic hydrogen gas, and molecular hydrogen gas in the gravitational field of the dark matter halo. The self-consistent vertical distribution for stars and gas in such a realistic system is obtained for radii between 4-22 kpc. The inclusion of an additional gravitating component constrains the vertical stellar distribution toward the mid-plane, so that the mid-plane density is higher, the disk thickness is reduced, and the vertical density profile is steeper than in the one-component, isothermal, stars-alone case. We show that the stellar distribution is constrained mainly by the gravitational field of gas and dark matter halo in the inner and the outer Galaxy, respectively. We find that the thickness of the stellar disk (measured as the HWHM of the vertical density distribution) increases with radius, flaring steeply beyond R=17 kpc. The disk thickness is reduced by a factor of 3-4 in the outer Galaxy as a result of the gravitational field of the halo, which may help the disk resist distortion at large radii. The disk would flare even more if the effect of dark matter halo were not taken into account. Thus it is crucially important to include the effect of the dark matter halo when determining the vertical structure and dynamics of a galactic disk in the outer region.

General model of vertical distribution of stars in the Milky Way using complete Jeans equations

“…Mid-plane density ρ 0 using the sech 2 model, model with only a non-flat, observed rotation curve (Model A) and the complete, general model (Model B) note that we have provided the ρ 0 values with higher decimal accuracy to facilitate comparison among various models, though the observed data is not known to this accuracy. Interestingly, we find that on inclusion of these kinematical terms, the resulting ρ(z) profiles are found to fit to a function of type sech 2/n with n varying with radius (as was also found for the case of multi-component model shown in Sarkar & Jog (2018)-which did not consider these kinematical effects), instead of the typical of sech 2 function.…”

“…This may be explained as follows. We expect that in the outer disc region, where the surface density is low and the vertical distribution becomes an extended one, as found in Sarkar & Jog (2018), the contribution of the radial gradient of potential may not be negligible compared to the vertical gradient in the Poisson equation. Further, the effect of R-z coupling and the planar random motions can have substantial effect on the vertical density distribution since the self-gravity of the disc becomes low.…”

“…The observed mean rotation velocity values (Sofue, 2012) are used in the last term in the above equation. The resulting mid-plane density ρ 0 values are listed in Table 1, under "Model A" and are compared with the results from sech 2 model (stars-alone case) obtained in Sarkar & Jog (2018), with ∆ A giving the % difference between these two models. We note that ρ 0 has increased at some radii (R=2,6,7 kpc) and has decreased at some radii (R=3,4,5 kpc) which happens due to the negative and positive gradient, respectively, present in the non-flat rotation curve at the corresponding radii.…”

“…Here, we attempt to solve for the vertical distribution of stars using the complete Poisson equation, where the vertical and radial terms are given in terms of complete vertical and radial Jeans equations without the usual simplifications -thus we can consider this as the complete and general model. We calculate the mid-plane density value and scaleheight of the disc, measured in terms of the half-width at half-maximum of the vertical density distribution, and compare them with the corresponding results obtained from a simple, stars-alone case (sech 2 model) as obtained from our earlier work (Sarkar & Jog, 2018). With the advent of accurate data, as from GAIA or LAMOST, it is feasible to check such modified density distribution with the observations, hence our study is timely.…”

“…We note that, as the velocity dispersion of stars falls with radius, its value may get less than the gas dispersion, beyond a certain radius. Since stars are formed from gas clouds, hence they cannot have a lower velocity dispersion than the gas itself, as explained in Sarkar & Jog (2018). The HI velocity dispersion in the outer Galaxy is observed to saturate around 7 kms −1 (Kamphuis 1993;Dickey 1996).…”